Since there are no appointments in San Francisco, I was planning to get the visa in India for which the trip is already planned.
Yes, you can apply in both places, you can visit consulate in your home country
Yes.
Make sure you get a pre booked itinerary for the schenegen visa applications They require a lot of documents and confirmation of travel plans. Also they only give you a Visa for X amount of days based on your Hotel booking, maybe a couple days extra. I got my schengen in Chennai in 2017
Were you also a US resident at that time ?
Yeah, I had a greencard at the time.
Switzerland denied my application in 2012 from Delhi and said I should've applied from the US as I work there. It's weird. Just apply from the US to be safe. And you need to book the tickets before hand. It costed me $500 to cancel my plans.
Are you serious ? What if there are no appointments left in USA?
Belgium told me they can give me a schengen visa from India. But then if I'd entered schengen territory from Switzerland, they might have asked questions or deny. Call the embassy/consulate in India for the country you're planning to enter. It's better than asking folks here.
You are Indian passport holder. You can do anything you want in India